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      <h1 class="mume-header" id="dss%E6%95%B0%E5%AD%97%E7%AD%BE%E5%90%8D%E6%A0%87%E5%87%86">DSS&#x6570;&#x5B57;&#x7B7E;&#x540D;&#x6807;&#x51C6;</h1>

<p><span id="toc"></span></p>
<ul>
<li><a href="#dss%E6%95%B0%E5%AD%97%E7%AD%BE%E5%90%8D%E6%A0%87%E5%87%86">DSS&#x6570;&#x5B57;&#x7B7E;&#x540D;&#x6807;&#x51C6;</a>
<ul>
<li><a href="#dsatoc">DSA</a>
<ul>
<li><a href="#dsa%E5%8F%82%E6%95%B0toc">DSA&#x53C2;&#x6570;</a>
<ul>
<li><a href="#dsa%E5%9F%9F%E5%8F%82%E6%95%B0toc">DSA&#x57DF;&#x53C2;&#x6570;</a></li>
</ul>
</li>
<li><a href="#dsa%E5%8F%82%E6%95%B0%E9%80%89%E6%8B%A9toc">DSA&#x53C2;&#x6570;&#x9009;&#x62E9;</a></li>
<li><a href="#dsa%E7%AD%BE%E5%90%8D%E7%94%9F%E6%88%90toc">DSA&#x7B7E;&#x540D;&#x751F;&#x6210;</a></li>
<li><a href="#dsa%E7%AD%BE%E5%90%8D%E7%9A%84%E9%AA%8C%E8%AF%81%E5%92%8C%E7%A1%AE%E8%AE%A4toc">DSA&#x7B7E;&#x540D;&#x7684;&#x9A8C;&#x8BC1;&#x548C;&#x786E;&#x8BA4;</a></li>
</ul>
</li>
<li><a href="#rsa%E6%95%B0%E5%AD%97%E7%AD%BE%E5%90%8D%E7%AE%97%E6%B3%95toc">RSA&#x6570;&#x5B57;&#x7B7E;&#x540D;&#x7B97;&#x6CD5;</a></li>
<li><a href="#ecdsa%E6%95%B0%E5%AD%97%E7%AD%BE%E5%90%8D%E7%AE%97%E6%B3%95toc">ECDSA&#x6570;&#x5B57;&#x7B7E;&#x540D;&#x7B97;&#x6CD5;</a></li>
<li><a href="#%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99toc">&#x53C2;&#x8003;&#x8D44;&#x6599;</a></li>
</ul>
</li>
</ul>
<h2 class="mume-header" id="dsatoc"><a href="#toc">DSA</a></h2>

<ul>
<li>&#x7B7E;&#x540D;&#x8FC7;&#x7A0B;:</li>
</ul>
<div class="mermaid">graph TD;
    id2 -.Signature.-&gt; id12

    subgraph Signature Generation;
    id0(Message/Data)-.-&gt; id1(Hash Function)
    id1 -.Message Digest.-&gt; id2(Sinature Generation)
    id3(Private Key) -.-&gt; id2
    end

    subgraph Signature Verification;
    id10(Message/Data)-.-&gt; id11(Hash Function)
    id11 -.Message Digest.-&gt; id12(Sinature Verification)
    id13(Public Key) -.-&gt; id12
    id12 -.-&gt; id14(Valid/Invalid)
    end
</div><ul>
<li>
<p>&#x521D;&#x59CB;&#x5316;&#x8BBE;&#x7F6E;:</p>
<ul>
<li>Obtain Domain Parameter;</li>
<li>Obtain Assurance of Domain Parameter Validity;</li>
<li>Obtain DS Key Pair;</li>
<li>Obtain Assurance of Public Key Validity;</li>
<li>Obtain Assurance of Possession of the DS Private Key;</li>
<li>Register the Public Key and Identify with a TTP(Optional);</li>
</ul>
</li>
<li>
<p>&#x6570;&#x5B57;&#x7B7E;&#x540D;&#x751F;&#x6210;:</p>
<ul>
<li>Generate a Message Digest;</li>
<li>Obtain Additional Information for the Digital Signature Process;</li>
<li>Generate a Digital Signature;</li>
<li>Verify the Digital Signature(Optional);</li>
</ul>
</li>
<li>
<p>&#x6570;&#x5B57;&#x7B7E;&#x540D;&#x7684;&#x9A8C;&#x8BC1;&#x548C;&#x786E;&#x8BA4;:</p>
</li>
</ul>
<div class="mermaid">graph LR;

    subgraph Actions;
    id1(Get the Claimed Signatory&apos;s Identifiers) -.-&gt; id2(Obtain the Domain Parameters and Public Key)
    id2 -.-&gt; id3(Generate a Message Digest)
    id3 -.-&gt; id4(Verify the Digital Signature)
    end

    subgraph Assurance;
    aid1(Obtain assurance of the Claimed Signatory&apos;s Identity)
    aid2(Obtain Assurance of Domain Parameter Validity) -.-&gt; aid3(Obtain Assurance of the Validity of the Owner&apos;s Public Key)
    aid2 -.-&gt; aid4(Obtain Assurance that the Owner Possesses the Private Key)
    end

    subgraph ValidationComplete;
    vid1(Digital Signature Validation Complete)
    end

    aid1 -.-&gt; vid1
    aid3 -.-&gt; vid1
    aid4 -.-&gt; vid1
    id4 -.-&gt; vid1
</div><h3 class="mume-header" id="dsa%E5%8F%82%E6%95%B0toc"><a href="#toc">DSA&#x53C2;&#x6570;</a></h3>

<ul>
<li>&#x516C;&#x94A5;<span class="mathjax-exps">$y=g^x\mod p$</span>;</li>
<li>&#x79C1;&#x94A5;<span class="mathjax-exps">$x\in [1,q-1]$</span>;</li>
<li>&#x7D20;&#x6570;<span class="mathjax-exps">$p$</span>, &#x4F4D;&#x957F;&#x5EA6;&#x4E3A;<span class="mathjax-exps">$L$</span>, <span class="mathjax-exps">$p\in (2^{L-1}, 2^L)$</span>;</li>
<li>&#x548C;<span class="mathjax-exps">$p-1$</span>&#x4E92;&#x8D28;&#x7684;&#x7D20;&#x6570;<span class="mathjax-exps">$q$</span>, &#x4F4D;&#x957F;&#x5EA6;&#x8BB0;&#x4E3A;<span class="mathjax-exps">$N$</span>, <span class="mathjax-exps">$q\in (2^{N-1}, 2^N)$</span>;</li>
<li>&#x4E58;&#x6CD5;&#x7FA4;<span class="mathjax-exps">$GF(p)$</span>&#x4E2D;&#x9636;&#x4E3A;<span class="mathjax-exps">$q$</span>&#x7684;&#x5B50;&#x7FA4;&#x7684;&#x751F;&#x6210;&#x5B50;<span class="mathjax-exps">$g$</span>, <span class="mathjax-exps">$g \in (1,p)$</span>;</li>
<li>&#x4F2A;&#x968F;&#x673A;&#x6574;&#x6570;<span class="mathjax-exps">$k$</span>, <span class="mathjax-exps">$k\in [1,q-1]$</span>;</li>
</ul>
<h4 class="mume-header" id="dsa%E5%9F%9F%E5%8F%82%E6%95%B0toc"><a href="#toc">DSA&#x57DF;&#x53C2;&#x6570;</a></h4>

<ul>
<li><span class="mathjax-exps">$p, q, g$</span>;</li>
<li>&#x53EF;&#x9009;&#x7684;<code>domain_parameter_seed/counter</code>, &#x7528;&#x4E8E;<span class="mathjax-exps">$p,q$</span>&#x7684;&#x751F;&#x6210;;</li>
</ul>
<h3 class="mume-header" id="dsa%E5%8F%82%E6%95%B0%E9%80%89%E6%8B%A9toc"><a href="#toc">DSA&#x53C2;&#x6570;&#x9009;&#x62E9;</a></h3>

<ul>
<li>&#x89C4;&#x8303;&#x6307;&#x5B9A;&#x7684;(L,N)&#x957F;&#x5EA6;&#x9009;&#x62E9;:
<ul>
<li>L = 1024, N = 160;</li>
<li>L = 2048, N = 224;</li>
<li>L = 2048, N = 256;</li>
<li>L = 3072, N = 256;</li>
</ul>
</li>
<li>&#x54C8;&#x5E0C;&#x51FD;&#x6570;&#x7684;&#x9009;&#x62E9;&#x8981;&#x6EE1;&#x8DB3;&#x5176;&#x5B89;&#x5168;&#x5F3A;&#x5EA6;&#x5927;&#x4E8E;<span class="mathjax-exps">$min(L,N)$</span>;</li>
</ul>
<h3 class="mume-header" id="dsa%E7%AD%BE%E5%90%8D%E7%94%9F%E6%88%90toc"><a href="#toc">DSA&#x7B7E;&#x540D;&#x751F;&#x6210;</a></h3>

<ul>
<li>&#x8BB0;Hash&#x51FD;&#x6570;&#x7684;&#x8F93;&#x51FA;&#x4F4D;&#x5B57;&#x7B26;&#x4E32;&#x7684;&#x4F4D;&#x957F;&#x5EA6;&#x4E3A;<span class="mathjax-exps">$outlen$</span>;</li>
<li>&#x8BB0;<code>truncate_l(bit_str, len)</code>&#x8868;&#x793A;&#x53D6;&#x4F4D;&#x5B57;&#x7B26;&#x4E32;<code>bit_str</code>&#x7684;&#x6700;&#x5DE6;&#x8FB9;&#x7684;<code>len</code>&#x4F4D;;</li>
<li><span class="mathjax-exps">$k^{-1}$</span>&#x8868;&#x793A;&#x5173;&#x4E8E;&#x968F;&#x673A;&#x6570;<span class="mathjax-exps">$k$</span>&#x7684;&#x6A21;<span class="mathjax-exps">$q$</span>&#x7684;&#x9006;, &#x5373;<span class="mathjax-exps">$(k^{-1}\cdot k)\mod q = 1$</span>;</li>
<li>&#x7B7E;&#x540D;<span class="mathjax-exps">$(r,s)$</span>&#x7684;&#x8BA1;&#x7B97;&#x5982;&#x4E0B;:</li>
</ul>
<p></p><div class="mathjax-exps">$$\begin{aligned} &amp; r = (g^k \mod p) \mod q \\ &amp; z = truncate_l(Hash(M), min(N, outlen)) \\ &amp; s = (k^{-1}(z+x\cdot r))\mod q; \end{aligned}$$</div><p></p>
<h3 class="mume-header" id="dsa%E7%AD%BE%E5%90%8D%E7%9A%84%E9%AA%8C%E8%AF%81%E5%92%8C%E7%A1%AE%E8%AE%A4toc"><a href="#toc">DSA&#x7B7E;&#x540D;&#x7684;&#x9A8C;&#x8BC1;&#x548C;&#x786E;&#x8BA4;</a></h3>

<ul>
<li>&#x5047;&#x8BBE;&#x8BA4;&#x8BC1;&#x8005;&#x5DF2;&#x7ECF;&#x786E;&#x8BA4;&#x4E86;&#x57DF;&#x53C2;&#x6570;&#x548C;&#x516C;&#x94A5;;</li>
<li>&#x8BB0;&#x63A5;&#x53D7;&#x8005;&#x6536;&#x5230;&#x4E86;&#x6D88;&#x606F;<span class="mathjax-exps">$M&apos;$</span>, &#x548C;&#x7B7E;&#x540D;<span class="mathjax-exps">$(r&apos;, s&apos;)$</span>, &#x5219;&#x7B7E;&#x540D;&#x9A8C;&#x8BC1;&#x5982;&#x4E0B;;
<ul>
<li>&#x7B7E;&#x540D;&#x9700;&#x6EE1;&#x8DB3;<span class="mathjax-exps">$0\lt r&apos; \lt q$</span>, <span class="mathjax-exps">$0 \lt s&apos; \lt q$</span>;</li>
<li><span class="mathjax-exps">$r&apos;$</span>&#x9700;&#x6EE1;&#x8DB3;<span class="mathjax-exps">$r&apos;=v$</span>:
<ul>
<li><span class="mathjax-exps">$w = (s&apos;)^{-1}\mod q$</span>;</li>
<li><span class="mathjax-exps">$z = truncate_l(Hash(M&apos;), min(N, outlen))$</span>;</li>
<li><span class="mathjax-exps">$u1 = (z\cdot w)\mod q$</span>;</li>
<li><span class="mathjax-exps">$u2 = (r&apos; \cdot w)\mod q$</span>;</li>
<li><span class="mathjax-exps">$v = ((g^{u1}\cdot y^{u2})\mod p) \mod q$</span>;</li>
</ul>
</li>
</ul>
</li>
</ul>
<h2 class="mume-header" id="rsa%E6%95%B0%E5%AD%97%E7%AD%BE%E5%90%8D%E7%AE%97%E6%B3%95toc"><a href="#toc">RSA&#x6570;&#x5B57;&#x7B7E;&#x540D;&#x7B97;&#x6CD5;</a></h2>

<ul>
<li>&#x516C;&#x94A5;<span class="mathjax-exps">$(n, e)$</span>;</li>
<li>&#x79C1;&#x94A5;<span class="mathjax-exps">$(n, d)$</span>;</li>
</ul>
<p>&#x76F8;&#x5173;&#x7684;&#x6807;&#x51C6;&#x6709;:</p>
<ul>
<li>ANS X9.31;</li>
<li>PKCS1;</li>
</ul>
<h2 class="mume-header" id="ecdsa%E6%95%B0%E5%AD%97%E7%AD%BE%E5%90%8D%E7%AE%97%E6%B3%95toc"><a href="#toc">ECDSA&#x6570;&#x5B57;&#x7B7E;&#x540D;&#x7B97;&#x6CD5;</a></h2>

<p>&#x76F8;&#x5173;&#x6807;&#x51C6;:</p>
<ul>
<li>ANS X9.62;</li>
</ul>
<h2 class="mume-header" id="%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99toc"><a href="#toc">&#x53C2;&#x8003;&#x8D44;&#x6599;</a></h2>

<ul>
<li>FIPS 186-4;</li>
</ul>

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